Problem 1286. MatCAT - Reconstruct X from Its X-rays

Created by Ned Gulley

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Last Solution submitted on Jul 18, 2023

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Alfonso Nieto-Castanon on 24 Feb 2013

regarding the discussion question, my guess is that the only cases where the answer becomes unique are those 'trivial' single-vector or equivalent cases. More precisely those cases where min(nnz(row_sums),nnz(col_sums))<=1. The reasons is that if one solution exist where x(a,b)>0 and x(c,d)>0 (and a~=c and b~=d; i.e. they are not in the same row or column), then you could simply subtract one from x(a,b) and x(c,d), and add one to x(c,b) and x(a,d), and the result will also be a valid solution... thoughts?

Andrea Caruso on 7 Nov 2020

Nice problem

锦 on 30 Jul 2022

good problem.

Armando Longobardi on 11 Nov 2022

See also this: https://it.mathworks.com/matlabcentral/cody/problems/47618

There is a nice video explaining how to solve these problems.

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Problem 1286. MatCAT - Reconstruct X from Its X-rays

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Problem 1286. MatCAT - Reconstruct X from Its X-rays

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